Exam 15: B:nonparametric Statistics

Attitude Test Narrative Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes. -Refer to Attitude Test Narrative. Using $\alpha$ = 0.10, can we conclude the motion picture was successful in changing attitudes?

Apply the Friedman test to the accompany table of ordinal data to determine whether we can infer at the 10% significance level that at least two population locations differ. Treatment

A vendor was interested in determining whether two soft drink machines dispense the same amount of liquid. A sample of size seven was selected from each machine and the amount of liquid dispensed (in mL) was recorded as follows: Use the Wilcoxon rank sum test to determine whether the distributions for the amount of liquid dispensed are the same for both machines. Use = 0.05.

Standardized College Entrance Exam Narrative Two psychometricians (educators who are experts in the field of psychological test design) were asked to rank six designs for a new standardized college entrance exam. Design This uses Spearman's rank correlation coefficient to see if there is a positive relationship between the educators' rankings. -Refer to Standardized College Entrance Exam Narrative. Find the rejection region for $\alpha$ = 0.05. NAR: Standardized College Entrance Exam Narrative

Advertisement Narrative In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: , , , , and . -Refer to Advertisement Narrative. What is the most accurate statement that can be made about the p-value of this test?

Gourmet Meals Narrative Two gourmets, A and B, rated 22 meals on a scale of 1 to 10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other? -Refer to Gourmet Meals Narrative. Use the large-sample z statistic for testing. (Note: Although the large-sample approximation is suggested for 25, it works fairly well for values of n as small as 15).

Teachers and Students' IQ Narrative. A school principal suspected that a teacher's attitude toward a Grade 1 student depended on his original judgment of the child's ability. The principal also suspected that much of that judgment was based on the Grade 1 student's IQ score, which was usually known to the teacher. After three weeks of teaching, a teacher was asked to rank the nine children in his class from 1 (highest) to 9 (lowest) as to his opinion of their ability. -Refer to Teachers and Students' IQ Narrative. Calculate for these teacher-IQ ranks.

Ice Cream Narrative A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand as better, 4 say that the brands taste the same, and the rest claim that the supermarket brand is better. -Refer to Ice Cream Narrative. Which test is appropriate for this situation?

Ice Cream Narrative A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand as better, 4 say that the brands taste the same, and the rest claim that the supermarket brand is better. -Refer to Ice Cream Narrative. Can we conclude at the 1% significance level that the general managers' claim is false? Justify your answer.

Customers' Ages Narrative The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlours, hamburger emporiums, and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed. Customers' Ages -Refer to Customers' Ages Narrative. Do these data provide enough evidence at the 10% significance level to infer that there are differences in ages among the customers of the three restaurants? Justify your response.

A randomized block design is used to compare three treatments in six blocks. Treatment a. Use the Friedman test to detect differences in location among the three treatment distributions. Test using = 0.05. b. Find the approximate p-value for the test in (a). c. Perform an analysis of variance and give the ANOVA table for the analysis, and using statistical software to approximate the p-value for the F-statistic in testing the equality of the three treatment means. Test using = 0.05. d. Compare the p-values for the tests in (b) and (c).

Attitude Test Narrative Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes. -Refer to Attitude Test Narrative. Describe what the test statistic is for the sign test. What is the value of the test statistic in this ?

Eight people were asked to perform a simple puzzle-assembly task under normal conditions and under stressful conditions. During the stressful time, a mild shock was delivered to subjects 3 minutes after the start of the experiment and every 30 seconds thereafter until the task was completed. Blood pressure readings were taken under both conditions. The data in the table are the highest readings during the experiment. Do the data present sufficient evidence to indicate higher blood pressure readings under stressful conditions? Analyze the data using the Wilcoxon signed-rank test for a paired experiment.

Teaching Methods Narrative Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another. -Refer to Teaching Methods Narrative. What is the observed significance level of this test?

Teaching Methods Narrative Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another. -Refer to Teaching Methods Narrative. State the null and alternative hypotheses.

Heart Rates and Exercise Narrative An experiment was conducted to examine the effect of age on heart rate when a person is subjected to a specific amount of exercise. Ten men were randomly selected from each of four age groups: 10-19, 20-39, 40-59, and 60-69. Each man walked a treadmill at a fixed grade for a period of 12 minutes, and the increase in heart rate (the difference before and after exercise) was recorded (in beats per minute). The data are shown in the table. -Refer to Heart Rates and Exercise Narrative. Do the data present sufficient evidence to indicate differences in location for at least two of the four age groups? Test using the Kruskal-Wallis H test with = 0.01.

Attitude Test Narrative Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes. -Refer to Attitude Test Narrative. State the null and alternative hypotheses.

Books Manuscripts Narrative In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better. -Refer to Books Manuscripts Narrative. What is the p-value of the test you conducted in the previous question?

Frozen TV Dinner Narrative The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below. Taste Ratings -Refer to Frozen TV Dinner Narrative. Can the general manager infer at the 5% significance level that there are differences in the taste ratings of the four dinners? Justify your decision.

Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 either to the left or to the right of distribution 2, based on samples of sizes = 7 and = 9. a. Should you use or as the test statistic? b. What is the rejection region for the test if c. What is the rejection region for the test if